Problem: Simplify. Rewrite the expression in the form $6^n$. $\dfrac{6^{4}}{6}=$
Solution: $\begin{aligned} \dfrac{6^{4}}{6}&=\dfrac{6^{4}}{6^1} \\\\ &=6^{4-1} \\\\ &=6^3 \end{aligned}$ This follows from the general rule $\dfrac{x^m}{x^n}=x^{m-n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} \dfrac{6^{4}}{6^1}&=\dfrac{\overbrace{\cancel 6\cdot 6\cdot 6\cdot 6}^\text{4 times}}{\underbrace{\cancel 6}_\text{1 time}} \\\\\\ &=\underbrace{6\cdot 6\cdot 6}_\text{3 times} \\\\ &=6^3 \end{aligned}$ In conclusion, $\dfrac{6^{4}}{6}=6^3$.